On the asymmetry of the past and the future of the ergodic ℤ-action

On the absence of multiple mixing and on the centralizer of measure-preserving actions

“…The results obtained in this paper also allow one to study the asymmetry in L-systems in the sense of [10] and [11].…”

On the asymmetry of multiple asymptotic properties of ergodic actions

“…Repeating arguments from [6], we obtain the following, formally more general, statement (in Yaroslavtsev's paper, the case N = 1 was studied).…”

“…Recently, Yaroslavtsev simplified the method of [2]. Let us quote the main statement of his paper [6].…”

“…, 0, 2N, N ) and the lengths of these arrays are unbounded. Then, by analogy with [6], for such a construction of T , for any fixed N , there exists a sequence h j → ∞ and a sequence of partitions of the phase space…”

“…The asymmetry of the asymptotic properties of flows was studied in [10]. Our paper, just as [6], was stimulated by the search for simplest and most illustrative invariants that show the difference between an action and its inverse. For ergodic theory, it is of interest that there is no interlacing between different positive powers of the transformation.…”